10 votes

Who introduced recurrence relations and sequences?

Depends on what "introduced" means. If we skip arithmetic and geometric series as too simple to suggest something general the idea goes back to Fibonacci and his rabbit breeding problem that ...
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9 votes
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Banach chicken story

You seem to be referencing the Scottish Book, and specifically problem 153 (whether all Banach spaces have the approximation property), for the solution of which Mazur promised a live goose as prize. ...
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  • 214
8 votes
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Who proved Banach fixed point theorem in abstract metric spaces for the first time?

Pages 97-107 of the book Mathematical Lives: Protagonists of the Twentieth Century From Hilbert to Wiles is an article by Guerraggio about Caccioppoli. On p. 100, Guerraggio says the contraction ...
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8 votes

Are there any records that show how Hilbert came to "invent" or "discover" Hilbert spaces?

The notion of Hilbert space comes from Hilbert's theory of integral equations. Of course, it was partially motivated by physics, by the theory of oscillations in classical mechanics, but this theory ...
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6 votes
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Are there any records that show how Hilbert came to "invent" or "discover" Hilbert spaces?

From Steen’s paper mentioned in a very similar MO question just yesterday: Hilbert himself was astonished that the spectra of his quadratic forms should come to be interpreted as atomic spectra. “...
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6 votes
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Who first proved the "acute angle principle" in fixed point theory?

Good sources on the history of fixed point theorems are Park, Ninety Years of the Brouwer Fixed Point Theorem and Kumar, A Short Survey of the Development of Fixed Point Theory. According to both, ...
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6 votes
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Who first proved that the spectrum of an operator is contained in the closure of its numerical range?

This is called the spectral inclusion theorem. Toeplitz's 1918 paper Das algebraische Analogon zu einem Satze von Fejér already has it for finite dimensional operators as Satz 4. This was before the ...
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4 votes
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Original mathematical foundation of Dirac's function

I found another, later paper which also references the Schwartz item that @sand1 commented as well as another paper by Schwartz from 1945. The reference paper is: Historia Mathematics 10 (1983) 149-...
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3 votes

What was Lipschitz's original motivation for the introduction of Lipschitz continuity?

It is existence and uniqueness question for ordinary differential equations. When I was a student (in 1970s) Lipschitz functions were not omnipresent in Analysis. The only context where this name ...
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2 votes
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Who proved the monotone convergence theorem for the Lebesgue integral?

The original version of the dominated convergence, from which the monotone convergence trivially follows assuming that the limit is Lebesgue integrable, was published by Lebesgue in Leçons sur l'...
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1 vote
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Who posed the separable quotient problem (and when)?

It seems the only firm fact about the origin of the problem is that it is discussed for the first time in print in 1969 in Rosenthal's On quasi-complemented subspaces of Banach spaces, without ...
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